Quantum theory of the strong magneto-optical effect of Ce-substituted yttrium iron garnet.

Abstract

Calculations of the Faraday rotation (FR) and ellipticity spectra in the wavelength region between 360 and 1260 nm caused by the ${\mathrm{Ce}}^{3+}$ ions in the Ce-substituted yttrium iron garnets based on the quantum theory are presented. The calculation of the temperature dependence of FR at 633 and 1150 nm wavelengths is presented as well. The Faraday effect contributed by the ${\mathrm{Ce}}^{3+}$ ions is caused mainly by the intraionic electrical dipole transitions between the 4f and 5d configurations. The effect of the crystal field (CF), superexchange interaction, and spin-orbit coupling on the magneto-optical (MO) effect has been discussed. The energy differences between the lowest and second CF-split 5d levels and the lowest CF-split 4f level are 1.36 and 3.10 eV, respectively. Therefore there are anomalous rotatory dispersions at about 1.36 and 3.10 eV. The difference of the transition intensity for the right- and left-handed circularly polarized light between the lowest CF-split 5d level and the ground state is negative, while the corresponding value for the transition between the second CF-split 5d level and the ground state is positive. So the FR is positive over the whole photon energy region between 1.36 and 3.10 eV and is negative outside this region. Since the energy differences between the CF splitting levels of the excited configuration are comparable with the energy difference between the mean energies of the excited and ground configurations, the MO coefficient varies with temperature. The admixing of different multiplets of the ground configuration is another cause which makes the MO coefficient vary with temperature.